Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.2 - The Limit of a Function - 2.2 Exercises: 7

Answer

(a) -1 (b) -2 (c) does not exist (d) 2 (e) 0 (f) does not exist (g) 1 (h) 3

Work Step by Step

(a) Looking at the graph, you can see that as the function approaches t=0 from the left side, g(t) = -1 (b) As the function approaches t=0 from the right side g(t)= -2 (c) The limit does not exist because as t approaches 0 from both sides, g(t) from the right side $\ne$ g(t) from the left side. (d) As the function approaches t=2 from the left side g(t)= 2 (e) As the function approaches t=2 from the right side g(t)= 0 (f) The limit does not exist because as t approaches 2 from both sides, g(t) from the right side $\ne$ g(t) from the left side. (g) At t=2, g(t) = 1 (h) As the function approaches t=4 from both sides g(t)=3 from the right side AND the left side. Therefore, $\lim\limits_{t \to 4}$ = 3
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